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Find the Cartesian equation of the locus...

Find the Cartesian equation of the locus whose parametric equations are `x=acostheta,y=asintheta` where `theta` is the parameter.

Text Solution

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The correct Answer is:
`a^(2)`
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Find the locus of the piont (acos^(3)theta,bsin^(3)theta) where theta is the parameter.

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Knowledge Check

  • The cartesian equation of the plane whose vector equation is

    A
    `2x+y=5`
    B
    `2x-y=5`
    C
    `2x-z=5`
    D
    `2x+z=5`.

  • The curve with parametric equation x=1 +4 cos theta, y=2 +3 sin theta is

    A
    an elipse
    B
    a parabola
    C
    a hyperbola
    D
    a circle

  • The locus of the point (a(costheta+sintheta),b(costheta-sintheta)) , where theta is the parameter, is

    A
    `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
    B
    `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
    C
    `(x^(2))/(a^(2))-(y^(2))/(b^(2))=2`
    D
    `(x^(2))/(a^(2))+(y^(2))/(b^(2))=2`

    • Similar Questions

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    Find the locus of the point (a-bsectheta,a-btantheta) where theta is the parameter.

    Find the locus of the point (acos^(4)theta,asin^(4)theta) where theta is a parameter.

    Locus of the point (cos theta +sin theta, cos theta - sin theta) where theta is parameter is

    Find the locus of point (tantheta+sintheta,tantheta-sintheta) where theta is a parameter.

    Locus of centroid of the triangle whose vertices are (acostheta,asintheta),(bsintheta,-bcostheta) and (2,0) where theta is a parameter is

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